Relationship between a natural number and its digital product

Laurențiu Panaitopol
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 10, 2004, Number 3, Pages 68—71
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Authors and affiliations

Laurențiu Panaitopol
University of Bucharest, Faculty of Mathematics
14 Academiei St., RO–010014 Bucharest, Romania

Abstract

For the integer number n ≥ 1 written in the basis b ≥ 2, we denote by s_b(n), p_b(n) and d_b(n) the sum, the product and the number of its digits, respectively. There are a series of more recent or older papers concerning the relationship between these numbers. For instance, one proves in {2} that, if b ≥ 3, then for infinitely many numbers m there exists n with d_b(n) = m and s_b(n) = m, and this property fails also for infinitely many values of m.

Keywords

Sums and products of digits
Inequalities
Means

AMS Classification

11A25
11A51

References

R.E. Kennedy, C. Cooper, A generalization of a result by Narkiewicz concerning large digits of powers. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 11(2000), 36–40 (2001).
L. Panaitopol, On the relation between the digital sum and product of a natural number (in press).

Cite this paper

APA

Panaitopol, L. (2004). Relationship between a natural number and its digital product. Notes on Number Theory and Discrete Mathematics, 10(3), 68-71.

Chicago

Panaitopol, Laurențiu. “Relationship between a Natural Number and Its Digital Product.” Notes on Number Theory and Discrete Mathematics 10, no. 3 (2004): 68-71.

MLA

Panaitopol, Laurențiu. “Relationship between a Natural Number and Its Digital Product.” Notes on Number Theory and Discrete Mathematics 10.3 (2004): 68-71. Print.